Question

Sides AB and AC of a triangle ABC are equal. BC is produced through C up to a point D such that AC = CD. D and A are joined and produced (through vertex A) up to point E. If angle BAE = 108°; find angle ADB.

Answer 1

In ΔABD,
∠BAE = ∠3 + ∠ADB
⇒ 108° = ∠3 + ∠ADB
But AB = AC
⇒ ∠3 = ∠2
⇒ 108° = ∠2 + ∠ADB ....……(i)

Now,
In ΔACD,
∠2 = ∠1 + ∠ADB
But AC = CD
⇒ ∠1 = ∠ADB
⇒ ∠2 = ∠ADB + ∠ADB
⇒ ∠2 = 2∠ADB

Putting this value in (i)
⇒ 108°  = 2∠ADB + ∠ADB
⇒ 3∠ADB = 108° 
⇒ ∠ADB = 36°